This paper proposes a set-theoretic receding horizon control scheme to address the trajectory tracking problem for input-constrained differential-drive robots. The proposed solution is derived starting from an inputoutput linearized description of the robot kinematics and a worst-case characterization of the orientation-dependent input constraint acting on the feedback linearized model. In particular, offline, given a worst-case characterization of the constraint set, we analytically design the smallest robust control invariant region for the tracking error. Moreover, such a region is recursively enlarged by computing a family of robust one-step controllable sets whose union characterizes the controller’s domain of attraction. Online, such sets and the knowledge of the current robot’s orientation are leveraged to define a non-conservative control law ensuring bounded tracking error. The effectiveness of the proposed strategy is experimentally validated using a Khepera IV robot, and its performance is contrasted with four alternative trajectory tracking algorithms.

C. Tiriolo, W. Lucia, "A Set-Theoretic Control Approach to the Trajectory Tracking Problem for Input-Output Linearized Wheeled Mobile Robots", IEEE Control Systems Letters, DOI 10.1109/LCSYS.2023.3286774, 2023